1. Field of the Invention
The present invention relates to a controlling apparatus utilized in various process instrumentation systems and, more particularly, to a controlling apparatus for, when a manipulative variable is deviated from one of upper and lower limit values and a change rate limit value, controlling a velocity-type I controlling output without omitting a velocity-type PD controlling output or a velocity-type P controlling output, so that the manipulative variable can be matched with various limitation conditions of a real process.
2. Description of the Related Art
PID (P: Proportional, I: Integral, D: Derivative) controlling apparatuses are widely utilized in instrumentation systems of various industrial fields, and are indispensable for plant operation control among these systems. A PID calculation method applied to the PID controlling apparatus is classified into analog and digital calculation methods. The digital calculation method is popular in the current PID controlling apparatuses.
A fundamental formula of a PID algorithm in the PID calculation method is expressed by: EQU MV=Kp{e+(1/T.sub.I).intg.edt+T.sub.D (de/dt)+MV.sub.0} ( 1)
where MV is the manipulative variable, e is the deviation, Kp is the proportional gain, T.sub.I is the integral time, T.sub.D is the derivative time, and MV.sub.0 is the initial value of the manipulative variable.
The digital calculation method using fundamental formula (1) has a predetermined sampling period .tau.. Necessary data is sampled for every sampling periods .tau. to execute calculations. Therefore, if the present sampling time is represented by n.tau. (n is an integer), and an immediately preceding sampling time is represented by (n-1).tau., a deviation at the present sampling time obtained from a control system can be expressed by e.sub.n, and a deviation at the immediately preceding sampling time can be expressed by e.sub.n-1.
The digital calculation method is classified into two ways of calculation methods. One method is a positional calculation method, and the other method is a velocity-type calculation method. In the positional calculation method, an overall manipulative variable MV.sub.n is directly calculated for each sampling period. In the velocity-type calculation method, in each sampling period, after a change .DELTA.MV.sub.n is calculated from an immediately manipulative variable, the change .DELTA.MV.sub.n is added to the immediately preceding manipulative variable MV.sub.n-1, thereby obtaining the present manipulative variable.
Therefore, when the positional calculation method is executed using fundamental formula (1) of the PID algorithm, the manipulative variable MV.sub.n is expressed by: ##EQU1## In the velocity-type calculation method, the manipulative variable MV.sub.n is expressed by:
.DELTA.MV.sub.n =Kp{(e.sub.n -e.sub.n -1)+(.tau./T.sub.I)e.sub.n +(T.sub.D /.tau.)(e.sub.n -2e.sub.n-1 +e.sub.n-2) (3a) EQU MV.sub.n =MV.sub.n-1 +.DELTA.MV.sub.n ( 3b)
These two formulas, i.e., formula (2) and formula (3) including equations (3a) and (3b) will be compared.
The velocity-type PID algorithm given by formula (3) has the following features:
(a) .SIGMA. is eliminated from an integral term, and a calculation can be simplified,
(b) upon switching between manual and automatic modes, after a manipulative variable obtained in the present manual operation is substituted in MV.sub.n-1 in equation (3b), automatic control is selected, and the change .DELTA.MV.sub.n is added to the variable MV.sub.n-1 from the next sampling time, so that control can be continued, and hence, balanceless-bumpless switching of manual-automatic switching can be easily attained,
(c) reset windup by an integral term can be easily performed, and
(d) since a change in manipulative variable need only be obtained, a gain can be easily corrected, and complex calculation processing with other variables can be easily performed.
Therefore, the velocity-type PID calculation method is frequently used in DDC (Direct Digital Control) using a computer.
In a controlling apparatus of this type, even if any of the analog calculation method, the positional digital calculation method, and the velocity-type digital calculation method is employed, when a manipulative variable becomes too large or too small, a plant is placed in a dangerous state. Thus, the manipulative variable has upper and lower limit values. Since it is not preferable to give an abrupt change to a downstream process, an operation terminal of a controlled system, or an amount of control of, e.g., steam, fuel, water, air, or the like, a manipulative variable is applied to the control signal while giving a certain limitation to a change rate of the manipulative variable. It is indispensable for the safety of a control system to limit a manipulative variable by giving an appropriate magnitude and change rate to it by the upper/lower limiting means and the change rate limiting means according to various limitation conditions and characteristics of a controlled system, and user's demands in control.
FIG. 1 is a block diagram of a conventional velocity-type PID controlling apparatus. In this apparatus, a deviation calculating means 1 subtracts a present process variable PV.sub.n of a controlled system 2 from a present target value SV.sub.n. The obtained deviation e.sub.n is supplied to a velocity-type PID controlling means 3. The velocity-type PID controlling means 3 performs a controlling calculation given by equation (3a), and outputs a velocity-type PID controlling output .DELTA.MV.sub.n. The velocity-type PID controlling output .DELTA.MV.sub.n is supplied to a change rate limiting means 4, and is limited within a predetermined change rate range, thereby outputting an output .DELTA.MV.sub.n '. The output .DELTA.MV.sub.n ' is then supplied to a velocity-to-positional signal converting means 5 with upper and lower limits, and is limited within a range between predetermined upper and lower limit values. The velocity-to-positional signal converting means 5 executes a calculation according to equation (3b), i.e., MV.sub.n =MV.sub.n-1 +.DELTA.MV.sub.n '. The obtained manipulative variable MV.sub.n is applied to the controlled system 2. Thus, the controlled system 2 is controlled to have the deviation e.sub.n =0, i.e., SV.sub.n =PV.sub.n.
As described above, when the PID controlling apparatus is applied to an actual process control system, a manipulative variable is largely changed by an abrupt change in target value SV.sub.n or an abrupt change in process variable PV.sub.n caused by a disturbance or the like. As a result, an abrupt change or an excessive manipulative amount is given to the controlled system 2, and this causes a damage and a decrease in service life of an operation terminal and piping system. Furthermore, upstream and downstream processes of the controlled system 2 are adversely influenced. In order to prevent this, the PID controlling apparatus comprises the change rate limiting means 4 and the velocity-to-positional signal converting means 5 to give a change rate limitation and upper and lower limitations to a manipulative variable. The PID controlling apparatus controls the manipulative variable using these means so that the controlled system 2 can be matched with various limitation conditions.
The controlling apparatus shown in FIG. 1 functionally gives a change rate limitation and upper and lower limitations to a manipulative variable. However, the method of limitation does not succeed "essence of PID control". As a result, the following industrially disadvantageous side effects occur when a manipulative variable is limited.
(1) When the deviation e.sub.n is changed stepwise or is pulsated and the PID controlling output .DELTA.MV.sub.n reaches a maximum point beyond an upper limit value, the manipulative variable is returned from its upper limit passing point by the P or D operation of the velocity-type PID controlling means 3. As a result, this leads to a control error or a decrease in safety. This is a serious industrial drawback.
A cause for this drawback will be explained in detail below. In FIG. 1, for example, when the deviation e.sub.n is changed stepwise, P+D operations mainly function at the beginning of the change. When there are no limitations at all in this case, the manipulative variable MV.sub.n behaves like a curve (a) in FIG. 2. However, in practice, the manipulative variable MV.sub.n is limited by an upper limit value H, and its Y portion is switched to a velocity-type signal. A decreased portion of the D operation is directly subtracted from the manipulative variable MV.sub.n. As a result, the manipulative variable MV.sub.n behaves like a curve (b) in FIG. 2. Although a behavior like a curve (c) in FIG. 2 is preferable, the manipulative variable MV.sub.n is largely returned from the upper limit passing point in practice. That is, the PD control functions in a reverse direction, and as a result, a control error occurs. After the manipulative variable is decreased to a region posing a problem in terms of safety, the manipulative variable is slowly restored to a normal state by the I operation.
(2) Even if the manipulative variable exceeds the upper or lower limit value and the deviation e.sub.n is large, when the target value SV.sub.n, the process variable PV.sub.n, and the like slightly fluctuate, the manipulative variable varies near the limit value. A cause for this variation will be explained below. Assume that the manipulative variable MV.sub.n is limited by the velocity-to-positional signal converting means 5 but the deviation e.sub.n slightly fluctuates in, e.g., a negative region, as shown in FIG. 3. In this case, when the output .DELTA.MV.sub.n ' of the change rate limiting means 4 changes to fall within the limitation range, the velocity-to-positional signal converting means 5 varies the output MV.sub.n to accept the output .DELTA.MV.sub.n '.
(3) When the deviation e.sub.n is changed stepwise or is pulsated and the manipulative variable exceeds the change rate limit value, a velocity-type signal of the P and D operations is omitted. As described above, the manipulative variable is returned by the D operation, and then comes closer to the target value SV.sub.n by the I operation. Therefore, a control response time is considerably prolonged, resulting in a serious industrial drawback.
A cause for this drawback will be explained below. The change rate limiting means 4 limits a unit updating amount by the velocity-to-positional signal converting means 5, and omits a first change in P+D operations. Since the change rate limiting means 4 subtracts a decrease produced by the D operation within the limitation range of the change rate, a manipulative variable MV is temporarily decreased and is then increased and saturated by only the I operation, like in MV of a curve (d) in FIG. 4. At the same time, a control response PV temporarily makes a counter response, and is then slowly increased and saturated by only the I operation, like in PV of a curve (e) in FIG. 4, resulting in a very long control response time.
In the conventional controlling apparatus, when a change in manipulative variable exceeds a change rate limit value or an upper or lower limit value, and is restored within a limitation range, inappropriate signal processing is performed, and a serious drawback is posed in practical applications.
A PID controlling apparatus of this type is widely utilized for control in a variety of fields such as plant instrumentation, and forms the basis of such control. When advanced plant operations, e.g., a flexible, optimized, or ultra-automated planet operation is to be realized in future, a change rate limitation and upper and lower limitations of a manipulative variable are indispensable, and a demand has arisen for advanced use of these limitation functions.